Hope y'all are enjoying N. VA! My last place of residence was Alexandria and it's an awesome region in my opinion.
I worked through everything in your list and a few other items related to steering/handling like replacing all shocks. Changing tires, unless you have big issues, shouldn't make a noticeable difference though lower inflation pressures (stay close to the recommended pressures on the hwy) could add some stability. I run around 30 or 32 psi and the door jamb recommends 32 for stock tires as I recall. The steering damper also probably won't make much if any difference in handling in most situations. It's good to know your caster to help you understand how the truck feels but I assume you are good there. Outside of those three items/areas every other item that I changed related to steering/suspension did make a noticeable difference to either steering tightness (lack of slack), sway or tracking (lack of wandering). Early on I mostly worked to get slack out of the system through tightening the steering box, bearings and replacing all rod ends. From there I replaced suspension bushings which resolved remaining wandering and further tightened steering feel a bit more also. Even the sway bar bushings which I did late in the game made a noticeable difference on my truck. I'll add that the first pair of shocks I installed were damped too softly and I would get dangerous body sway with a heavy on-board load. Stock/OE shocks ride great and resolved this for me.
A good next step for you may be to have it put on an alignment machine so that you can have your caster/toe checked and listed out clearly on paper. It's a relatively cheap step to help you assess those settings before you pursue more fixes. Then, as you drive it, develop your sense of how much of the bad handling is from sway, wandering/poor tracking and/or slack in the steering. Pay attention to how acceleration and deceleration impact tracking as they could be clues to where you have slack in the system. Also watch for how the truck sways and tracks or wanders over bumps and through turns, particularly at hwy speeds.
On my truck the end goal was for it to handle predictably on a few specific high-speed, bumpy/rolling turns that I take periodically. These are essentially interstate interchanges that are easily driven at 60+mph but that have developed enough 'character' to activate the suspension during the turn. Before replacing all of the suspension bushings the suspension articulation during the turn would steer the truck slightly back and forth, requiring steering wheel input to stay in the lane. The slight slack in the sway bar bushings compounded the problem because the truck would sway back and forth through the sway bar slack as it wandered back and forth. Adding a lot of onboard weight or a trailer and it was a poignant driving experience. Early in my repairs I experienced this same sensation even on straight but uneven roads, in cross-winds, etc. Every repair either reduced the wandering, swaying or amount of slack in the steering which made it easier to deal with. The truck now tracks and drives easily in all of these conditions including with a trailer attached or a full cargo area.
You'll likely need to replace all aged components to totally dial in your trucks handling. At the end of the process it will still handle like a solid axle truck but will be predictable and easy to manage. If you replace components a few at a time as I did you will develop a nice feel for how each impacts handling